Sampling Distributions · Superchallenge problem

Lab 1 measures a quantity $n_1 = 25$ times with an instrument of SD $10$; Lab 2 measures it $n_2 = 100$ times with an instrument of SD $30$. All measurements are independent and unbiased. The labs combine their sample means as $w\bar x_1 + (1-w)\bar x_2$. What is the smallest possible variance of this combined estimate? Express your answer as a common fraction.